Capturing handwriting on an LCD using some form of pen sensor has previously been performed by calculating the pen position and drawing a vector or spline from the last known pen position. The algorithm for drawing the vector or spline typically involves simply turning pixels on the curve on or off as appropriate. The resultant effect of such drawing is aliasing, i.e., a rather jagged line at the LCD screen resolutions of 90 dpi (dots per inch) which are commonly used today.
Greyscale, which is the use of levels of grey rather than simply black and white, makes an image appear to be of higher resolution than it actually is and can help to create the appearance of smoother lines in a pen-based computer. In this specification the term `n-level greyscale` means the actual number of greyscale levels, not the number of bits needed to store each greyscale value. For example, 4-level greyscale would require 2 bits of storage.
One known approach utilizing greyscale to achieve anti-aliasing of lines drawn on computer screens is the `partial inking` approach and a useful reference is a book titled `Computer Graphics: Principles and Practice` published by Addison Wesley, 1990. Partial inking involves calculating the ink level for pixels according to what fraction of the pixel would be covered by the (theoretical) line being drawn. This is a relatively crude approach which has the advantage of being low in cost but which is rather limited in the quality of result which can be achieved.
Another approach utilizing greyscale, and the one that is relevant to the present invention, involves digital sampling and filtering.
Generally, to render an image on a computer screen, the image must be sampled, i.e., digitized. The aliasing is the direct effect of sampling a continuous image which includes frequencies above the Nyquist limit. For a sampling frequency of f, the maximum frequency of the continuous image must be less than f/2. If this condition is not met, the sampling of higher frequencies causes extra, low frequency, components to be created which distort the resultant image. To prevent this problem, the continuous image needs to be passed though a low pass filter that cuts off at f/2 before sampling.
The article by Blinn entitled "What we need around here is more aliasing" in the IEEE Computer Graphics and Applications, 9(1): 75-79, January 1989 is helpful background reference material on the general topic of anti-aliasing.
Considering the problem of rendering freehand input onto a computer screen, it is desirable to render at the finest possible resolution, i.e., line widths of one pixel. However, this is the worst case for digitization distortions because then the freehand lines jump between full width and negligible width along their length.